Transcript Suitable for high level 5, or low level 6? Must know how to expand single brackets, and understand division operator Should not.

Suitable for high level 5, or low level 6?
Must know how to expand single brackets, and understand division operator
Should not be scared of seeing things like,
Even if they have not met quite that difficulty before
Standards Unit A2:
Creating and solving equations
.
Students need to.
1 to 2 hours. Teams of.
My.
Consumable Resources Needed:
Each student needs a single A4 worksheet + lots of spares. Students might want
to try it quite a few more times. And can also be used a a revision activity in
later lessons, once they understand the process of using the sheets.
Lots of copies of second worksheet. Expect many students (pairs) to progress to
this, but do not give it to them at the start. Let them progress to this level in
their own time.
Lots of copies of third worksheet. Expect some students (pairs) to progress to
this, but do not give it to them at the start. Let them progress to this level in
their own time.
Re-usable Resources Needed:
Minin-whitebaords
Camera?
FOLD ALONG THIS LINE
FOLD ALONG THIS LINE
FOLD ALONG THIS LINE
Build your 2nd equation
Operations
Operations
=
=
..........
..........
..........
..........
..........
..........
..........
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Check you’ve made no errors
Check you’ve made no errors
Substitute your original value into
the final equation.
Substitute your original value into
the final equation.
FOLD ALONG THIS LINE
Build your 1st equation
FOLD ALONG THIS LINE
Building harder equations!
FOLD ALONG THIS LINE
Name: . . . . . . . . . . . . . . . .
Name of Partner: . . . . . . . . . . . . . . . .
Solving harder equations
Solve 1st equation
Solve 2nd equation
Copy 1st
equation to
here
Copy 2nd
equation to
here
Solution
..........
..........
..........
..........
..........
..........
..........
..........
..........
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..........
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=
Solution
=
Mark your partner’s work. Did they follow your steps and get the
correct answer? What difficulties do you think they had?
Build your 1st equation
Build your 2nd equation
Operations
Operations
..........
..........
..........
..........
..........
..........
..........
..........
..........
..........
..........
Check.
=
..........
Check.
FOLD ALONG THIS LINE
=
FOLD ALONG THIS LINE
Building equations on your own
FOLD ALONG THIS LINE
Name: . . . . . . . . . . . . . . . .
Name of Partner: . . . . . . . . . . . . . . . .
Solving harder equations on your own
Solve 1st equation
Solve 2nd equation
Copy 1st
equation to
here
Copy 2nd
equation to
here
Solution:
..........
..........
..........
..........
..........
..........
..........
..........
..........
..........
..........
..........
Solution:
Mark your partner’s work. Did they follow your steps and get the
correct answer? What difficulties do you think they had?
Important that when modelling, I do NOT simplify. This would make
reversing the process much harder. i.e. Write
Students can start with mini-whiteboard which they can use from the
start to show each step of an equation being built. I should not do too
much correcting or assessing on their work at this stage. We want a
speedy start. It’s just getting them involved and thinking.
Mini-whiteboards needed at end too.
Pre-assign partners too.
Differentiation. More able students can use square and square root
operations too. They could also use fractions, or negative numbers. They
should also use more ‘steps’. Less able should not use division operator
when building equation, and need only use two or three steps initially.
Pre-distribute worksheets, possibly in plastic folders to stop too much
playing at start.
But useful for them to see the format of worksheet whilst working
through even early examples.
Solving Harder Equations
We will be learning to solve hard equations, but first
we’ll look at things in reverse, by building complex
equations starting from their solution!
What does the solution to an equation normally look like?
Letters
x
y
…
Building an Equation
Start with a solution!
Equation is ‘solved’!
Becoming more
complicated!
Operations
+
−
×
÷
Numbers
1
2
3
4
5
6
7
8
9
10
Becoming simpler
Check the equation:
substitute x=3 back in
Letters
x
y
…
Operations
+
−
×
÷
Building an equation together
We start with the Solution to an equation!
Equation is ‘solved’!
Becoming more
complicated!
Numbers
1
2
3
4
5
6
7
8
9
10
Becoming simpler
How did we build that equation?
The final equation we built was:
It tells the story of ‘a day in the life of’ the letter
What happened to it FIRST?
What happened next?
Can you tell be looking only at the equation?
How would we solve that equation?
Solving our Equation
Our final equation was:
Build Your Own Equations
LHS of worksheet
Build two equations of your own.
Then check that they really work!
Do not go on to the RHS yet.
Solving Your Partner’s Equations
RHS of worksheet
Before passing your worksheet to your partner:
1. Copy your final equations onto the RHS.
2. Fold worksheet so that partner cannot
immediately see your earlier work
If you get a bit stuck, ask your partner for help. But
try NOT to look back over the other side until you
have solved it.
When finished, pass back again.
Now complete question 5.
Please answer in as much detail as possible. It will
help me plan future lessons.
Choose what to do next
Have another go at Worksheet 1
Try the harder, guided Worksheet 2
6 steps rather than 4.
Free-style (unguided) Worksheet 3
You can also…
- use fractions, or negative numbers as well as the digits 1 to 10
- use squaring, or square roots, as well as + - x /
- even use reciprocal (1/x) and ‘change the sign’ (+/-) operations
- trig functions etc.
Write one of your favourite equations here
Working with your partner, choose one of the above
equations and solve it.
Then write your solution beside the corresponding equation above.
Assessment: ‘Think of a number’
Use mini-whiteboards individually, but work with a partner if you wish
Q1
I am thinking of a number. Call it
Q2
n
I am thinking of a number. Call it
Double it.
Add four.
Divide your answer by seven.
Multiply your answer by two.
The result is 4.
Show me your equation
Correct solution:
The result is
Show me your equation